5) Consider the vector ū =(1, 2, –2) and the points Q(5, 5, 2) and R(3,0,0).5.1) Find the equation of the plane P that contains R, and is orthogonal to v.5.2) Find the distance d between Q and P.5.3) Find the orthogonal projection ū of RQ, onto the plane P.5.4) Find the coordinates of the point S on the plane P, where the distance betweenS and Q is the value d (that you obtained in Question 5.2).

Answered: Image /qna-images/answer/492cdbff-bf8f-4f33-aa81-56320619df2d.jpg

5) Consider the vector ū = (1,2, –2) and the points Q(5, 5, 2) and R(3, 0,0). 5.1) Find the equation of the plane P that contains R, and is orthogonal to ū. 5.2) Find the distance d between Q and P.

5) Consider the vector ū = (1,2, –2) and the points Q(5, 5, 2) and R(3, 0,0). 5.1) Find the equation of the plane P that contains R, and is orthogonal to ū. 5.2) Find the distance d between Q and P.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 13CR

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Question

5) Consider the vector ū =
(1, 2, –2) and the points Q(5, 5, 2) and R(3,0,0).
5.1) Find the equation of the plane P that contains R, and is orthogonal to v.
5.2) Find the distance d between Q and P.
5.3) Find the orthogonal projection ū of RQ, onto the plane P.
5.4) Find the coordinates of the point S on the plane P, where the distance between
S and Q is the value d (that you obtained in Question 5.2).

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